Option Theory: A Synthesis
Keywords:
option pricing, Black-Scholes, real options, financial derivatives, exotic options, option theoryAbstract
Option pricing dates back to the turn of the century with Bachelier's doctoral dissertation on speculation theory. In 1964 Bonness developed a formula for option pricing similar in nature to that of Black-Scholes's but that relied upon an unknown interest rate. It was not until 9 years later that Black and Scholes came up with a formula to price European options, which would revolutionize financial theory. Unlike most theoretical breakthroughs, Black-Scholes's formula became increasingly popular among practitioners, and nowadays it is widely used in the main exchanges around the world.
In recent years Hull, White and Rubinstein, among many others, have worked on pricing the so-called exotic options. Meanwhile Trigeorgis, Brennan, Schwartz and others have illustrated how option theory can be used in assessing the profitability of investment opportunities -real options. Option theory has been also applied to the pricing of many other financial instruments, such as warrants, callable bonds, and callable-convertibles bonds.
The aim of this paper is to discuss the progress that option theory has made since Black and Scholes developed their seminal formula. We will review the most outstanding models, mention some numerical methods used in option pricing when no analytical solution exist, and discuss the importance of real options as a new technique for assessing investment opportunities.
Downloads
References
Acworth, P., Broadie, M., & Glasserman, P. (1996). A comparison of some Monte Carlo and quasi Monte Carlo techniques for option pricing. In H. Niederreiter, P. Hellekalek, G. Larcher, & P. Zinterhof (Eds.), Monte Carlo and quasi Monte Carlo methods (Lecture Notes in Statistics, Vol. 127, pp. 15–29). Springer.
Aït-Sahalia, Y. (1996a). Non-parametric pricing of interest rate derivative securities. Econometrica, 64(3), 527–560.
Aït-Sahalia, Y. (1996b). Testing continuous-time models of the spot interest rate. The Review of Financial Studies, 9(2), 385–426.
Amin, K., & Ng, V. (1997). Inferring future volatility from the information in implied volatility in Eurodollar options: A new approach. The Review of Financial Studies, 10(2), 333–367. https://doi.org/10.1093/rfs/10.2.333
Bharadia, M., Christofides, N., & Salkin, G. (1995). Computing the Black-Scholes implied volatility: Generalization of a simple formula. In P. Boyle, F. Longstaff, & P. Ritchen (Eds.), Advances in futures and options research (Vol. 8). JAI Press.
Baxter, M., & Rennie, A. (1996). Financial calculus. Cambridge University Press. https://doi.org/10.1017/cbo9780511806636
Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81(3), 637–654. https://doi.org/10.1086/260062
Boness, A. J. (1964). Elements of a theory of stock-option values. Journal of Political Economy, 72(2), 163–175.
Brennan, M., & Schwartz, E. (1985). Evaluating natural resource investments. Journal of Business, 58(2), 135–157.
Clarke, H., & Reed, W. (1989). The tree-cutting problem in a stochastic environment. Journal of Economic Dynamics and Control, 13(4), 569–595.
Cox, J., Ross, S., & Rubinstein, M. (1979). Option pricing: A simplified approach. Journal of Financial Economics, 7(3), 229–263.
Cox, J., Ingersoll, J., Jr., & Ross, S. A. (1985). A theory of the term structure of interest rates. Econometrica, 53(2), 385–467.
Chan, K. C., Karolyi, A., Longstaff, F. A., & Sanders, A. B. (1992). An empirical comparison of alternative models of the short-term interest rate. The Journal of Finance, 47(3), 1209–1227. https://doi.org/10.2307/2328983
Chu, S., & Freund, S. (1996). Volatility estimation for stock index options: A GARCH approach. Quarterly Review of Economics and Finance, 36(4), 431–450. https://doi.org/10.1016/s1062-9769(96)90044-7
Derman, E., & Kani, I. (1994a). The volatility smile and its implied tree (Quantitative Strategies Research Notes). Goldman Sachs.
Derman, E., & Kani, I. (1994b). Riding on the smile. Risk, 7, 32–39.
Dixit, A., & Pindyck, R. S. (1994). Investment under uncertainty. Princeton University Press.
Dumas, B., Fleming, J., & Whaley, R. (1998). Implied volatility functions: Empirical tests. The Journal of Finance, 53(6), 2059–2106. https://doi.org/10.1111/0022-1082.00083
Dupire, B. (1994). Pricing with a smile. Risk, 7, 18–20.
Engle, R. F. (Ed.). (1995). ARCH selected readings. Oxford University Press.
Fernández, P. (1996). Opciones, futuros e instrumentos derivados. Ediciones Deusto.
Fernández, V. (1999a). Valorización de derivados (Trabajo Docente N.º 64). Instituto de Economía, Pontificia Universidad Católica de Chile.
Fernández, V. (1999b). Estructura de tasas de interés en Chile: La vía no-paramétrica. Cuadernos de Economía, 36(109).
Figlewski, S., Silber, W., & Subrahmanyam, M. (Eds.). (1990). Financial options: From theory to practice. McGraw Hill.
Geske, R. (1979). The valuation of compound options. Journal of Financial Economics, 7(1), 63–81. https://doi.org/10.1016/0304-405x(79)90022-9
Gong, F. F., & Remolona, E. M. (1997). A three-factor econometric model of the U.S. term structure (Staff Reports 19). Federal Reserve Bank of New York.
Hamilton, J. D. (1994). Time series analysis. Princeton University Press.
Heath, D., Jarrow, R., & Morton, A. (1992). Bond pricing and the term structure of interest rates: A new methodology. Econometrica, 60(1), 77–105. https://doi.org/10.2307/2951677
Herzel, S. (1998). A simple model for option pricing with jumping stochastic volatility. International Journal of Theoretical and Applied Finance, 1(4), 487–505. https://doi.org/10.1142/s0219024998000266
Ho, T. S., & Lee, S. B. (1986). Term structure movements and pricing interest rate contingent claims. The Journal of Finance, 41(5), 1011–1029. https://doi.org/10.1111/j.1540-6261.1986.tb02528.x
Hull, J. (1997). Options, futures, and other derivatives (3.ª ed.). Prentice Hall.
Hull, J., & White, A. (1992). Extensions of the binomial tree approach for valuing path-dependent options (Working Paper) [Mimeo]. University of Toronto.
Hull, J., & White, A. (1987). The pricing of options on assets with stochastic volatilities. Journal of Finance, 42(2), 281–300. https://doi.org/10.1111/j.1540-6261.1987.tb02568.x
Jarrow, R., & Rudd, A. (1982). Approximate option valuation for arbitrary stochastic processes. Journal of Financial Economics, 10(3), 347–369. https://doi.org/10.1016/0304-405x(82)90007-1
Jarrow, R., & Wiggins, J. (1989). Option pricing and implicit volatilities. Journal of Economic Surveys, 3(1), 59–81. https://doi.org/10.1111/j.1467-6419.1989.tb00058.x
Jiang, G. (1998). Non-parametric modeling of U.S. interest rate term structure dynamics and implications on the prices of derivative securities. Journal of Financial and Quantitative Analysis, 33(4), 465–497.
Karolyi, G. A. (1993). A Bayesian approach to modeling stock return volatility for option valuation. Journal of Financial and Quantitative Analysis, 28(4), 579–594.
Kemna, A., & Vorst, A. (1990). A pricing method for options based on average asset values. Journal of Banking and Finance, 14(1), 113–129. https://doi.org/10.1016/0378-4266(90)90039-5
Li, J. (1999). Quasi-Monte Carlo algorithm for pricing options (Working Paper). Department of Mathematics and Statistics, Pennsylvania State University.
Longstaff, F. A., & Schwartz, E. S. (1992). The interest rate volatility and the term structure: A two-factor general equilibrium model. The Journal of Finance, 47(3), 1259–1282. https://doi.org/10.2307/2328939
McAfee, R. (1998). Four issues in auctions and market design. Revista de Análisis Económico, 13(1), 7–24.
McAfee, R., & McMillan, J. (1987). Auctions and bidding. The Journal of Economic Literature, 25(2), 699–738.
McDonald, R., & Siegel, D. (1986). The value of waiting to invest. Quarterly Journal of Economics, 101(4), 707–728. https://doi.org/10.2307/1884175
Merton, R. (1998). Applications of option-pricing theory: Twenty-five years later. The American Economic Review, 88(3), 323–349.
Merton, R. (1976). Option pricing when underlying returns are discontinuous. Journal of Financial Economics, 3(1-2), 125–144. https://doi.org/10.1016/0304-405x(76)90022-2
Merton, R. (1973). Theory of rational option pricing. Bell Journal of Economics and Management Science, 4(1), 141–183. https://doi.org/10.2307/3003143
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 1999 Viviana Fernández M.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Article usage
- ViewsTimes this article's page was opened since the journal started recording statistics. One person can visit more than once.
- 106
- DownloadsTimes the full text of this article (usually the PDF) was opened or downloaded.
- 143
All time, as recorded by the journal.
Last 2 years: 40 views, 74 downloads.
1.35 downloads per view (journal average 1.65).Downloads of the full text for every abstract view of this article, compared with the whole journal.
Explore the journal's metrics
